On the spin-observables in pseudoscalar meson photoproduction

Abstract

Spin-observables in pseudoscalar meson photoproduction is discussed. This work is complementary to the earlier works on this topic. Here, the reaction amplitude is expressed in Pauli-spin basis which allows to calculate all the observables straightforwardly. We make use of the fact that the underlying reflection symmetry about the reaction plane can be most conveniently and easily exploited in this basis to help finding the non-vanishing and independent observables in this reaction. The important issue of complete experiments is reviewed. By expressing the reaction amplitude in Pauli-spin basis, many sets of eight observables -distinct from those found in earlier works from the amplitude in transversity basis -capable of determining the reaction amplitude up to an overall phase are found. It is also shown that some of the combinations of the spin observables are suited for studying certain aspects of the reaction dynamics. We, then, carry out a (strictly) model-independent partialwave analysis, in particular, of the peculiar angular behavior of the beam asymmetry observed in η ′ photoproduction very close to threshold [P. Levi Sandri et al. 2015 Eur. Phys. J. A 51, 77]. This work should be useful, especially, for newcomers in the field of baryon spectroscopy, where the photoproduction reactions are a major tool for probing the baryon spectra.Spin-observables in pseudoscalar meson photoproduction [7,12,13,14,15,16,17,18,19,20,21] (for some of the related earlier works, see, e.g., Refs. [22,23,24] ). Of particular interest in this connection is the issue of whether the baryon resonances can be extracted model independently or with minimal model requirements. Efforts along this line is currently in progress [15,16,19,20].In this work, we consider those same issues mentioned above; as such, it is complementary to the earlier works on this topic [1,3,4,5,6,7]. In contrast to those studies, we consider the photoproduction amplitude in Pauli-spin basis which allows us to calculate the spin-observables, in general, in a straightforward and quite pedestrian way. We will make used of the underlying reflection symmetry about the reaction plane -which can be conveniently and easily exploited in this basis -to help find the non-vanishing observables in this reaction. Also, the Pauli-spin amplitude is simply related to that of the usual Chew-Goldberger-Low-Nambu (CGLN) form [28] due to this symmetry. The important and non-trivial issue of the complete experiments is reviewed. In particular, by using Pauli-spin representation of the reaction amplitude instead of transversity representation, we identify other sets of observables, not reported in [5,8], for complete experiments. In addition, certain combinations of the observables are shown to be useful in isolating (low) partial-wave states to learn about the reaction dynamics. Motivated by this, a model-independent analysis of the η ′ photoproduction off the proton close to threshold is performed in connection to the peculiar angular behavior exhibited by the beam asymmetry in...

Nucleon and $Δ$ resonances in $γn \to K^+Σ^-$ photoproduction

“…More data are needed to further learn about the resonance content in this reaction. In fact, we mention that a pseudoscalar-meson photoproduction process requires at least eight carefully chosen independent observables to determine the corresponding reaction amplitude up to an overall phase [57][58][59].…”

Spin asymmetries in quasielastic charged current neutrino-nucleon scattering

“…They contain information about the structure of the scattering amplitude and the structure of the particles participating in the interaction. The meson photoproduction is a good example of the process for which the spin observables are utilized to constrain the form of the scattering amplitude [5,6]. Another example is the elastic ep scattering.…”

“…6 M 4 + 8m 4 M 2 (−m 2 + 6M 2 )t + m 2 (m 4 − 144M 4 )t 2 − 2su 3 t 2 +(−3m 4 + 24m 2 M 2 + 80M 4 )t 3 + (3m 2 − 16M 2 )t 4 − t 5 + su 2 t(−4m 2 M 2 + (−3m 2 + 20M 2 )t + t 2 ) +2su(8m4 M 4 − 6m 4 M 2 t + 4M 2 (3m 2 − 2M 2 )t 2 + (−m 2 − 6M 2 )t 3 + t 4 ))x ] M 4 + 8m 2 M 2 (−m 2 − 4M 2 )t − su 3 t + su 2 (4M 2 − t)t +(m 4 + 16m 2 M 2 + 16M 4 )t 2 + 2(−m 2 − 4M 2 )t 3 + t 4 +su(−4m 4 M 2 + m 2 (m 2 + 8M 2 )t + 2(−m 2 − 2M 2 )t 2 + t 3 ))x ] A 3 t(−(su 3 t) + 2su 2 (2m 2 M 2 + (−m 2 − 2M 2 )t + t 2 ) +su(4m 4 M 2 − m 4 t − 4M 2 t 2 + t 3 ) + 2(−16m 4 M 4 + 8m 2 M 2 (m 2 + 4M 2 )t + (−m 4 − 16m 2 M 2 − 16M 4 )t 2 +2(m 2 + 4M 2 )t 3 − t 4 )) + F A 3 F P t(−4m 6 M 2 + m 4 (m 2 + 12M 2 )t + su 3 t + 3m 2 (−m 2 − 4M 2 )t 2 +(3m 2 + 4M 2 )t 3 − t 4 + su 2 t(−m 2 + t) + su(4m 4 M 2 + m 2 (−m 2 − 8M 2 )t + 2(m 2 + 2M 2 )t 2 − t 3 ))x + F A 3 F A t(−4m 6 M 2 + 2su 3 (2M 2 − t) + m 4 (m 2 + 12M 2 )t + 3m 2 (−m 2 − 4M 2 )t 2 + (3m 2 + 4M 2 )t 3 − t 4 +su 2 (8m 2 M 2 − 3m 2 t + t 2 ) + 2su(−16m 2 M 4 + 8M 2 (m 2 + 2M 2 )t + (−m 2 − 8M 2 )t 2 + t 3 ))x ] (s − M 2 )I [ (F V 1 + F V 2 )F P t(−4m 6 M 2 + m 4 (m 2 + 12M 2 )t + 3m 2 (−m 2 − 4M 2 )t 2 +(3m 2 + 4M 2 )t 3 − t 4 + su 2 t(m 2 + t) + 2su(−2m 4 M 2 + m 4 t + (−m 2 + 2M 2 )t 2 )) + 4F V 1 F A M 2 (4m 4 M 2 (m 2 − 8M 2 ) + m 2 (−m 4 + 4m 2 M 2 + 64M 4 )t + su 3 t + (m 4 − 20m 2 M 2 − 32M 4 )t 2 +(m 2 + 12M 2 )t 3 − t 4 + su 2 (4m 2 M 2 + (m 2 − 4M 2 )t + t 2 ) +su(8m 4 M 2 + m 2 (−m 2 − 16M 2 )t + 2(m 2 + 4M 2 )t 2 − t 3 )) + F V 2 F A (su 3 (8M 2 − t)t + 2su 2 t(8m 2 M 2 + (−m 2 − 4M 2 )t + t 2 ) + su(16m 4 M 4 + 4m 2 M 2 (m 2 − 16M 2 )t +(−m 4 + 8m 2 M 2 + 48M 4 )t 2 − 12M 2 t 3 + t 4 ) + 2(8m 6 M 4 + 2m 4 M 2 (−m 2 − 20M 2 )t +14m 2 M 2 (m 2 + 4M 2 )t 2 + (−m 4 − 22m 2 M 2 − 24M 4 )t 3 + 2(m 2 + 5M 2 )t 4 − t 5 )) + F 2 P m 2 t(−4m 4 M 2 + m 2 (m 2 + 8M 2 )t − su 2 t + 2(−m 2 − 2M 2 )t 2 + t 3 )x + 4F 2 A M 2 (4m 4 M 2 (−m 2 + 4M 2 ) + m 2 (m 4 − 32M 4 )t + (−m 4 + 12m 2 M 2 + 16M 4 )t 2 − (m 2 + 8M 2 )t 3 +t 4 + su 2 (−4m 2 M 2 + m 2 t − t 2 ) + 2m 2 su(−4m 2 M 2 + (m 2 + 4M 2 )t − t 2 ))x + F V 2 2 (16m 6 M 4 − 8m 4 M 2 (m 2 + 6M 2 )t + m 2 (m 4 + 28m 2 M 2 + 48M 4 )t 2 − su 3 t 2 − 4(m 4 + 8m 2 M 2 + 4M 4 )t 3 +(5m 2 + 12M 2 )t 4 − 2t 5 + sut 2 (m 2 (−m 2 + 8M 2 ) − 8M 2 t + t 2 ) + su 2 t(4m 2 M 2 − (3m 2 + 4M 2 )t + 2t 2 ))x M 2 (2(−m 2 + 2M 2 )su 2 t − su 3 t + sut(m 2 (−m 2 + 8M 2 ) − 8M 2 t + t 2 ) +4M 2 (4m 4 M 2 + m 2 (−m 2 − 8M 2 )t + 2(m 2 + 2M 2 )t 2 − t 3 ))x + F A F P t(4M 2 su 2 (−m 2 − t) − su 3 t + 2m 2 (−4m 4 M 2 + m 2 (m 2 + 8M 2 )t + 2(−m 2 − 2M 2 )t 2 + t 3 ) +su(−12m 4 M 2 + m 2 (3m 2 + 16M 2 )t + 4(−m 2 − M 2 )t 2 + t 3 ))x + F V 1 F V 2 (16m 6 M 4 + 8m 4 M 2 (−m 2 − 2M 2 )t + m 2 (m 4 + 16m 2 M 2 − 16M 4 )t 2 −2su 3 t 2 + (−3m 4 − 8m 2 M 2 + 16M 4 )t 3 + 3m 2 t 4 − t 5 + su 2 t(−4m 2 M 2 + (−3m 2 + 4M 2 )t + t 2 ) +2su(8m 4 M 4 − 6m 4 M 2 t + 4M 2 (3m 2 − 2M 2 )t 2 + (−m 2 − 6M 2 )t 3 + t 4 ))x ] (C84) A 3 t(su 3 t + 2su 2 (−2m 2 M 2 + (m 2 + 2M 2 )t − t 2 ) +su(−4m 4 M 2 + m 4 t + 4M 2 t 2 − t 3 ) + 2(16m 4 M 4 + 8m 2 M 2 (−m 2 − 4M 2 )t + (m 4 + 16m 2 M 2 + 16M 4 )t 2 +2(−m 2 − 4M 2 )t 3 + t 4 )) + F A 3 F A t(4m 6 M 2 + m 4 (−m 2 − 12M 2 )t + 3m 2 (m 2 + 4M 2 )t 2 + (−3m 2 − 4M 2 )t 3 + t 4 + 2su 3 (−2M2 + t) +su 2 (−8m 2 M 2 + 3m 2 t − t 2 ) + 2su(16m 2 M 4 + 8M 2 (−m 2 − 2M 2 )t + (m 2 + 8M 2 )t 2 − t 3 ))x + F A 3 F P t(4m 6 M 2 + m 4 (−m 2 − 12M 2 )t − su 3 t + su 2 (m 2 − t)t + 3m 2 (m 2 + 4M 2 )t 2 + (−3m 2 − 4M 2 )t 3 +t 4 + su(−4m 4 M 2 + m 2 (m 2 + 8M 2 )t + 2(−m 2 − 2M 2 )t 2 + t 3 ))x ] (C86)…”